• Bulletin of the Korean Mathematical Society
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• v.58 no.2
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• pp.481-495
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• 2021

In this paper, we investigate the properties of Bergman spaces, Bloch spaces and integral means of p-harmonic functions on the unit ball in ℝn. Firstly, we offer some Lipschitz-type and double integral characterizations for Bergman space ��kγ. Secondly, we characterize Bloch space ��αω in terms of weighted Lipschitz conditions and BMO functions. Finally, a Hardy-Littlewood type theorem for integral means of p-harmonic functions is established.

• Korean Journal of Mathematics
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• v.8 no.2
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• pp.135-138
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• 2000

In this paper, we study harmonic orientation-preserving univalent mappings defined on ${\Delta}=\{z:{\mid}z{\mid}>1\}$ that are typically real.

• Korean Journal of Mathematics
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• v.20 no.4
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• pp.433-439
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• 2012

In this paper, we study harmonic, orientation-preserving, univalent mappings defined on ${\Delta}$ = {z : |z| > 1} that have real coefficients or starlike analytic functions and obtain some coefficients bounds.

• Kyungpook Mathematical Journal
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• v.50 no.3
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• pp.433-445
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• 2010

Although, interesting properties on the partial sums of analytic univalent functions have been investigated extensively by several researchers, yet analogous results on partial sums of harmonic univalent functions have not been so far explored. The main purpose of the present paper is to establish some new and interesting results on the ratio of starlike harmonic univalent function to its sequences of partial sums.

• Journal of the Korean Mathematical Society
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• v.51 no.3
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• pp.567-592
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• 2014

Complex-valued harmonic functions that are univalent and sense-preserving in the open unit disk are widely studied. A new methodology is employed to construct subclasses of univalent harmonic mappings from a given subfamily of univalent analytic functions. The notions of harmonic Alexander operator and harmonic Libera operator are introduced and their properties are investigated.

• Kyungpook Mathematical Journal
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• v.55 no.1
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• pp.83-89
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• 2015

In the present paper, we introduce new subclasses of harmonic univalent functions and establish certain results concerning the convolution of functions for these subclasses. Relevant connections of the results presented here with various known results are briefly indicated.

• Honam Mathematical Journal
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• v.40 no.3
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• pp.433-446
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• 2018

In this present investigation, we introduce a new class of harmonic univalent functions of the form $f=h+{\bar{g}}$ in the open unit disk ${\Delta}$. We get basic properties, like, necessary and sufficient convolution conditions, distortion bounds, compactness and extreme points for these classes of functions.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.31 no.3 s.258
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• pp.300-305
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• 2007

Many practical flow problems are defined with the circular boundary. Fluid flows within a circular boundary are however susceptible to a singularity problem when the cylindrical coordinates are employed. To remove this singularity a method has been developed in this study which uses the local harmonic functions in discretization of derivatives as well as interpolation. This paper describes the basic reason for introducing the harmonic functions and the overall numerical methods. The numerical methods are evaluated in terms of the accuracy and the stability. The Lamb-dipole flow is selected as a test flow. We will see that the harmonic-function method indeed gives more accurate solutions than the conventional methods in which the polynomial functions are utilized.

• Korean Journal of Mathematics
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• v.11 no.2
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• pp.79-84
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• 2003

In this paper, we obtain the sharp estimates for co-efficients of harmonic, orientation-preserving, univalent mappings defined on ${\Delta}=\{z:{\mid}z{\mid}>1\}$ when harmonic mappings are of bounded variation on ${\mid}z{\mid}=1$.

• Korean Journal of Mathematics
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• v.11 no.2
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• pp.85-91
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• 2003

On the setting of the upper half-space of the euclidean space $\mathbf{R}^n$, we show some properties of weighted harmonic Bergman functions.